Calculation of sound propagation in nonuniform flows

Suppression of instability waves

Anurag Agarwal, Philip John Morris, Ramani Mani

Research output: Contribution to journalArticle

103 Citations (Scopus)

Abstract

Acoustic waves propagating through nonuniform flows are subject to convection and refraction. Most noise prediction schemes use a linear wave operator to capture these effects. However, the wave operator can also support instability waves that, for a jet, are the well-known Kelvin-Helmhotz instabilities. These are convective instabilities that can completely overwhelm the acoustic solution downstream of the source location. A general technique to filter out the instability waves is presented. A mathematical analysis is presented that demonstrates that the instabilities are suppressed if a time-harmonic response is assumed, and the governing equations are solved by a direct solver in the frequency domain. Also, a buffer-zone treatment for a nonreflecting boundary condition implementation in the frequency domain is developed. The outgoing waves are damped in the buffer zone simply by adding imaginary values of appropriate sign to the required real frequency of the response. An analytical solution to a one-dimensional model problem, as well as numerical and analytical solutions to a two-dimensional jet instability problem, are provided. They demonstrate the effectiveness, robustness, and simplicity of the present technique.

Original languageEnglish (US)
Pages (from-to)80-88
Number of pages9
JournalAIAA journal
Volume42
Issue number1
DOIs
StatePublished - Jan 1 2004

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Acoustic waves
Refraction
Mathematical operators
Acoustics
Boundary conditions

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering

Cite this

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abstract = "Acoustic waves propagating through nonuniform flows are subject to convection and refraction. Most noise prediction schemes use a linear wave operator to capture these effects. However, the wave operator can also support instability waves that, for a jet, are the well-known Kelvin-Helmhotz instabilities. These are convective instabilities that can completely overwhelm the acoustic solution downstream of the source location. A general technique to filter out the instability waves is presented. A mathematical analysis is presented that demonstrates that the instabilities are suppressed if a time-harmonic response is assumed, and the governing equations are solved by a direct solver in the frequency domain. Also, a buffer-zone treatment for a nonreflecting boundary condition implementation in the frequency domain is developed. The outgoing waves are damped in the buffer zone simply by adding imaginary values of appropriate sign to the required real frequency of the response. An analytical solution to a one-dimensional model problem, as well as numerical and analytical solutions to a two-dimensional jet instability problem, are provided. They demonstrate the effectiveness, robustness, and simplicity of the present technique.",
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Calculation of sound propagation in nonuniform flows : Suppression of instability waves. / Agarwal, Anurag; Morris, Philip John; Mani, Ramani.

In: AIAA journal, Vol. 42, No. 1, 01.01.2004, p. 80-88.

Research output: Contribution to journalArticle

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